An explosive demand for data network bandwidth emerged within the last two decades as the use of internet and other related data services increased. This demand exponentially grows at a rate close to 60% per year. This growth rate is not about to slow down considering large bandwidth consuming data services such as cloud computing, multi-media real-time applications etc. are expected to gain importance. The demand for network traffic was economically enabled by wavelength-division multiplexing (WDM) technologies researched and developed in the early 90's. At start, the WDM allowed the optical transport throughput to grow at a rate of 80% per year. However, in the last decade this growth rate experienced a dramatic slow-down to about 20%. This was explained by recent studies on the non-linear Shannon capacities of optical fibers where it was shown that current optical transport systems approach their fundamental limits to within a factor of 2.
It is thus clear that new strategies need to be found to continue supporting the ever growing demand for data network. To that end, intense research efforts were directed in the last years to find new strategies beyond WDM. Multiplexing techniques such as time-division multiplexing (TDM), complex modulation and more recently, polarization-division multiplexing (PDM), were employed in the latest generation of optical systems. The only physical dimension left to be exploit is space. Recent studies showed that space-division multiplexing (SDM) is currently the only known method that allows a substantial increase in optical transport capacities and yet is economically attractive. Thus SDM technology is considered today to be the most promising strategy for next generation optical systems satisfying the network growth for the next decade and beyond.
SDM strategies in wireless communication, where multiple antennas are used at the transmitter and/or receiver, have been extensively researched in the last two decades. The most common statistical model of the wireless channel is the Rayleigh fading—the path gain between each transmit and receive antennas is assumed to have a Normal distribution whereas all path gains are independent. Many important works have been conducted in this field where the capacity, error and outage probabilities were comprehensively analyzed. A further fundamental tradeoff in spatially multiplexed wireless systems was defined and analyzed—the tradeoff between multiplexing, exploiting the multiple antennas for higher transmission rate, and diversity, achieving better error probability by transmitting the same signal through multiple paths.
In optical communication an SDM system uses m parallel transmission paths per wavelength which optimally multiplies the potential throughput of a certain link by a factor of m.
Since m can potentially be chosen very large, SDM technology is highly scalable. These parallel optical paths could be multiple single-mode fiber strands within a fiber cable, multiple cores within a multi-core fiber, or multiple modes within a multi-mode waveguide. In this work we consider the multi-mode fiber, however results are applicable also in all other SDM optical structures.
Now, significant crosstalk between the independent optical paths raises the need for multiple-input multiple-output (MIMO) techniques. However, signal processing for large size MIMO schemes (large m) is currently not feasible in the optical rates. Assuming that higher rates signal processing will be available in the future and having in mind that the procedure of replacing optical fibers to support SDM is long and expensive, one will want to make a long term design. To that end and more, it was proposed to design an optical system that can support relatively large number of paths for future use, but at start to address only some of the paths. Winzer and Foschini discuss this Jacobi channel where simulations of the capacities and outage probabilities were presented. The importance of addressing all paths was shown—zero outage probability can be attained for any transmission rate only when all paths are addressed both at the transmitter and receiver. The outage probability is an important measure in optical systems and is required to be very low. Thus, choosing the number of addressed paths is a very critical design step that highly reflects on the system outage.